Rahul Mazumder

SparseNet: Coordinate Descent With Nonconvex Penalties

We address the problem of sparse selection in linear models. A number of nonconvex penalties have been proposed in the literature for this purpose, along with a variety of convex-relaxation algorithms for finding good solutions. In this article we pursue a coordinate-descent approach for optimization, and study its convergence properties. We characterize the properties of penalties suitable for this approach, study their corresponding threshold functions, and describe a df-standardizing reparametrization that assists our pathwise algorithm. The MC+ penalty is ideally suited to this task, and we use it to demonstrate the performance of our algorithm. Certain technical derivations and experiments related to this article are included in the Supplementary Materials section.

Best subset selection via a modern optimization lens

In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We present a MIO approach for solving the classical best subset selection problem of choosing

LEAST QUANTILE REGRESSION VIA MODERN OPTIMIZATION

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Non-negative matrix completion for bandwidth extension: A convex optimization approach

out of

A Computational Framework for Multivariate Convex Regression and Its Variants

p

MODELING ITEM-ITEM SIMILARITIES FOR PERSONALIZED RECOMMENDATIONS ON YAHOO! FRONT PAGE

features in linear regression given

Assessing the significance of global and local correlations under spatial autocorrelation: A nonparametric approach

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Turbulence, suspension and downstream fining over a sand-gravel mixture bed

observations. We develop a discrete extension of modern first order continuous optimization methods to find high quality feasible solutions that we use as warm starts to a MIO solver that finds provably optimal solutions. The resulting algorithm (a) provides a solution with a guarantee on its suboptimality even if we terminate the algorithm early, (b) can accommodate side constraints on the coefficients of the linear regression and (c) extends to finding best subset solutions for the least absolute deviation loss function. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with

A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives

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Fluid flow pattern analysis in a trough region: a nonparametric approach

in the 1000s and